(CBS News) The White House immigration plan that would reportedly allow undocumented immigrants to become legal U.S. residents within eight years is being circulated among President Obama's administration in case the bipartisan efforts of Congress to draft a comprehensive reform bill "break down," the president's chief of staff Denis McDonough said today on "Face the Nation."

"We will be prepared with our own plan," McDonough said, in the event that the so-called "gang of eight" senators - including Sens. John McCain, R-Ariz., Chuck Schumer, D-N.Y., and Marco Rubio, R-Fla. - fail to push their immigration proposals through both the Democrat-controlled Senate and the Republican-controlled House.

One major discord from the president is that the senators maintain Congress needs to improve on enforcing current laws and tightening U.S. border control before opening up a pathway to citizenship for illegal immigrants.

"There's no evidence that [the group's efforts] have broken down yet," he continued. "We're continuing to support that; we're involved in those efforts by providing them technical assistance, providing them ideas. And I hope that Republicans and Democrats up there don't get involved in some typical Washington back and forth sideshow here, and rather just roll up their sleeves and get to work on writing a comprehensive immigration reform bill."

As laid out in his speech several weeks ago in Las Vegas, McDonough said, Mr. Obama's plan would include four pillars: Continue to strengthen U.S. border security, crack down on employers who hire illegal workers, offer a path to earned citizenship for the 11 million undocumented immigrants currently living in the United States and reform the current legal immigration system.

Meantime, McDonough went on the defensive over the White House's response to the Sept. 11, 2012, attack on the U.S. Consulate in Benghazi that killed four Americans. Last week on "Face the Nation," Sen. Lindsey Graham, R-S.C. pledged to block confirmation votes for Chuck Hagel and John Brennan to head the Department of Defense and the CIA, respectively, until the president provided details about his actions on the night of the attack.

"We did everything we could that night," McDonough argued, "which, by the way, was borne out by the Accountability Review Board which Secretary [of State Hillary] Clinton stood up to look at this. They said that... the Washington-based effort was a good effort that did everything it possibly could have.

"But the question from the president now is," he continued, "what have we done to make sure that this does not happen again? And he's demanded of us, his team, be that at State Department, be that at the White House or at the Pentagon or the intelligence community, to make sure this never happens again. And he won't put up with it."